If '+' means 'x', '÷' means '-', '-' means '+', and 'x' means '÷'. Which of the following will be the value of the expression? $12+5-24\times3 \div 5$
Expression Evaluation with Symbol Substitution
This solution explains how to solve the given mathematical expression by replacing operators according to the defined rules and then evaluating the result using the standard order of operations.
Symbol Replacements Defined
The problem provides a set of rules for symbol substitution:
| Original Symbol | Replacement Symbol |
|---|---|
| + | × |
| ÷ | - |
| - | + |
| × | ÷ |
Applying Operator Changes
The original expression is $12+5-24\times3 \div 5$. Applying the substitution rules yields a new expression:
- The '+' sign is replaced by '×'.
- The '-' sign is replaced by '+'.
- The '×' sign is replaced by '÷'.
- The '÷' sign is replaced by '-'.
Therefore, the expression transforms into: $12 \times 5 + 24 \div 3 - 5$
Evaluating the New Expression
The modified expression $12 \times 5 + 24 \div 3 - 5$ is evaluated using the order of operations (BODMAS/PEMDAS):
- Division: Perform the division first.
$24 \div 3 = 8$
The expression becomes: $12 \times 5 + 8 - 5$ - Multiplication: Next, perform the multiplication.
$12 \times 5 = 60$
The expression simplifies to: $60 + 8 - 5$ - Addition: Perform the addition.
$60 + 8 = 68$
The expression is now: $68 - 5$ - Subtraction: Finally, perform the subtraction.
$68 - 5 = 63$
The value of the evaluated expression is 63.
Important Questions from Mathematical Operations
What will come in the place of ‘?’ in the following equation if ‘+’ and ‘−’ are interchanged and ‘×’ and ‘÷’ are interchanged?
18 ÷ 9 + 24 × 3 − 16 = ?If ‘A’ stands for ‘÷’, ‘B’ stands for ‘×’, ‘C’ stands for ‘+’, and ‘D’ stands for ‘−’, what will come in place of the question mark (?) in the following equation?
88 B 3 D 12 A 4 C 6 = ?Select the set in which the numbers are related in the same way as are the numbers of the given sets.
(NOTE: Operations should be performed on whole numbers without breaking down the numbers into their constituent digits. E.g., 13 – Operations on 13 such as adding/subtracting/multiplying, etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
Given sets:
(9, 21, 193)
(12, 15, 184)What will come in the place of the question mark (?) in the following equation, if ‘÷’ and ‘+’ are interchanged and ‘−’ and ‘×’ are interchanged?
44 ÷ 78 + 6 − 3 × 19 = ?Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
